An Interpretable Approach to PDE Solution Discovery via Structural Experience Distillation

The paper introduces SED-MCTS, a Monte Carlo tree search method that enhances PDE solution discovery by distilling structural experience from evaluated expressions. Unlike previous approaches that rely on a single terminal score, SED-MCTS uses counterfactual subtree interventions to estimate local structural contributions, guiding the search toward reliable construction edges and preserving useful components in a structural archive. The method extends naturally to coupled multiphysics systems and demonstrates improved performance, efficiency, and robustness across diverse PDE benchmarks, especially under noisy or scarce observations.

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